Using Baumgarte's Method for Index Reduction in Modelica

We show by example how Baumgarte’s method can be used in a Modelica model to reduce the differential algebraic equation index prior to compilation. This has advantages for some constrained mechanical systems especially those with closed-chain kinematics, including improved initialization and enabling model-based control system design. We derive models for a simple pendulum, a delta robot and for elevator cable sway as case studies. The models are used for simulation and also for dynamic analysis and to design and realize feedback controllers.